dc.contributor.author Chen, W. dc.contributor.author Wang, Song dc.date.accessioned 2017-04-28T13:57:06Z dc.date.available 2017-04-28T13:57:06Z dc.date.created 2017-04-28T09:06:07Z dc.date.issued 2017 dc.identifier.citation Chen, W. and Wang, S. 2017. A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing. Applied Mathematics and Computation. 305: pp. 174-187. dc.identifier.uri http://hdl.handle.net/20.500.11937/52000 dc.identifier.doi 10.1016/j.amc.2017.01.069 dc.description.abstract © 2017 Elsevier Inc.In this paper we propose a power penalty method for a linear complementarity problem (LCP) involving a fractional partial differential operator in two spatial dimensions arising in pricing American options on two underlying assets whose prices follow two independent geometric Lévy processes. We first approximate the LCP by a nonlinear 2D fractional partial differential equation (fPDE) with a penalty term. We then prove that the solution to the fPDE converges to that of the LCP in a Sobolev norm at an exponential rate depending on the parameters used in the penalty term. The 2D fPDE is discretized by a 2nd-order finite difference method in space and Crank–Nicolson method in time. Numerical experiments on a model Basket Option pricing problem were performed to demonstrate the convergent rates and the effectiveness of the penalty method. dc.publisher Elsevier Inc. dc.title A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing dc.type Journal Article dcterms.source.volume 305 dcterms.source.startPage 174 dcterms.source.endPage 187 dcterms.source.issn 0096-3003 dcterms.source.title Applied Mathematics and Computation curtin.department Department of Mathematics and Statistics curtin.accessStatus Fulltext not available
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